Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht - PowerPoint PPT Presentation

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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht These slides related to Griffiths section 1.3. Consider the following group of people in a room:. Histogram Form. Consider the following group of people in a room:. Total people = 14.

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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht

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Working with probabilities physics 115a slideshow 1 a albrecht

Working with Probabilities

Physics 115a (Slideshow 1)

A. Albrecht

These slides related to Griffiths section 1.3


Working with probabilities physics 115a slideshow 1 a albrecht

Consider the following group of people in a room:


Working with probabilities physics 115a slideshow 1 a albrecht

Histogram Form


Working with probabilities physics 115a slideshow 1 a albrecht

Consider the following group of people in a room:

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Consider the following group of people in a room:

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Consider the following group of people in a room:

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Consider the following group of people in a room:

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Consider the following group of people in a room:

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Consider the following group of people in a room:

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Consider the following group of people in a room:

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Probability Histogram


Working with probabilities physics 115a slideshow 1 a albrecht

Number Histogram


Working with probabilities physics 115a slideshow 1 a albrecht

NB: The probabilities for ages not listed are all zero

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Assuming Age<20, what is the probability of finding each age?

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Assuming Age<20, what is the probability of finding each age?

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Assuming Age<20, what is the probability of finding each age?

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Assuming no age constraint, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Assuming Age<20, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14


Working with probabilities physics 115a slideshow 1 a albrecht

Consider a different room with different people:

Total people = 15


Working with probabilities physics 115a slideshow 1 a albrecht

Consider a different room with different people:

Total people = 15


Working with probabilities physics 115a slideshow 1 a albrecht

Red Room Numbers


Working with probabilities physics 115a slideshow 1 a albrecht

Red Room Probabilities


Working with probabilities physics 115a slideshow 1 a albrecht

Combine Red and Blue rooms

Total people = 29


Working with probabilities physics 115a slideshow 1 a albrecht

  • Lessons so far

  • A simple application of probabilities

  • Normalization

  • “Re-Normalization” to answer a different question

  • Adding two “systems”.

  • All of the above are straightforward applications of intuition.


Working with probabilities physics 115a slideshow 1 a albrecht

Expectation Values


Working with probabilities physics 115a slideshow 1 a albrecht

Most probable answer = 25

Median = 23

Average = 21


Working with probabilities physics 115a slideshow 1 a albrecht

Most probable answer = 25

Median = 23

Average = 21

Lesson: Lots of different types of questions (some quite similar) with different answers. Details depend on the full probability distribution.


Working with probabilities physics 115a slideshow 1 a albrecht

Average (mean):

  • Standard QM notation

  • Called “expectation value”

  • NB in general (including the above) the “expectation value” need not even be possible outcome.


Working with probabilities physics 115a slideshow 1 a albrecht

Average (number squared)


Working with probabilities physics 115a slideshow 1 a albrecht

Careful: In general

In general, the average (or expectation value) of some function f(j) is


Working with probabilities physics 115a slideshow 1 a albrecht

The “width” of a probability distribution


Working with probabilities physics 115a slideshow 1 a albrecht

Discuss eqns 1.10 through 1.13 at board


Working with probabilities physics 115a slideshow 1 a albrecht

Continuous Variables


Working with probabilities physics 115a slideshow 1 a albrecht

Continuous Variables

Why not measure age in weeks?


Working with probabilities physics 115a slideshow 1 a albrecht

Blue room in weeks


Working with probabilities physics 115a slideshow 1 a albrecht

Blue room in weeks


Working with probabilities physics 115a slideshow 1 a albrecht

Conclusion: Blue room in weeks not very useful/intuitive


Working with probabilities physics 115a slideshow 1 a albrecht

Another case where a measure of age in weeks might by useful:

The ages of students taking health in the 8th grade in a large school district (3000 students).


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